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1.
We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping Theorem for Banach spaces is then combined with Michael's Selection Theorem to yield the existence of a continuous bounded positively homogeneous right inverse of such a surjective map; a strong version of the usual Open Mapping Theorem is then a special case. As another consequence, an improved version of the analogue of Andô's Theorem for an ordered Banach space is obtained for a Banach space that is, more generally than in Andô's Theorem, a sum of possibly uncountably many closed not necessarily proper cones. Applications are given for a (pre)-ordered Banach space and for various spaces of continuous functions taking values in such a Banach space or, more generally, taking values in an arbitrary Banach space that is a finite sum of closed not necessarily proper cones. 相似文献
2.
L. M. García. Raffi E. A. Sánchez. Pérez J. V. Sánchez. Pérez 《Integral Equations and Operator Theory》2006,54(4):495-510
Let λ be a countably additive vector measure with values in a separable real Hilbert space H. We define and study a pseudo metric on a Banach lattice of integrable functions related to λ that we call a λ-weighted distance.
We compute the best approximation with respect to this distance to elements of the function space by the use of sequences
with special geometric properties. The requirements on the sequence of functions are given in terms of a commutation relation
between these functions that involves integration with respect to λ. We also compare the approximation that is obtained in
this way with the corresponding projection on a particular Hilbert space. 相似文献
3.
It is shown that for every separable Banach space X with non-separable dual, the space contains an unconditional family of size . The proof is based on Ramsey Theory for trees and finite products of perfect sets of reals. Among its consequences, it
is proved that every dual Banach space has a separable quotient. 相似文献
4.
We introduce and investigate the weak metric approximation property of Banach spaces which is strictly stronger than the approximation
property and at least formally weaker than the metric approximation property. Among others, we show that if a Banach space
has the approximation property and is 1-complemented in its bidual, then it has the weak metric approximation property. We
also study the lifting of the weak metric approximation property from Banach spaces to their dual spaces. This enables us,
in particular, to show that the subspace of c0, constructed by Johnson and Schechtman, does not have the weak metric approximation property.
The research of the second-named author was partially supported by Estonian Science Foundation Grant 5704 and the Norwegian
Academy of Science and Letters. 相似文献
5.
Guillermo P. Curbera 《Indagationes Mathematicae》2006,17(2):187-204
New features of the Banach function space L1w(v), that is, the space of all v-scalarly integrable functions (with v any vector measure), are exposed. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract Banach lattices. Applications are also given to the optimal domain of kernel operators taking their values in a Banach function space. 相似文献
6.
《Journal of Functional Analysis》2007,247(1):138-168
We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out. 相似文献
7.
Bagrat T. Batikyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(2):77-86
The paper studies the branching A-index and the topological branching index of points of the spectrum of Arens-Hoffman algebraic extension of a semisimple commutative Banach algebras A. 相似文献
8.
9.
Petr Hájek 《Journal of Differential Equations》2010,249(12):3342-3351
We show that if X is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping f:X→X such that the autonomous differential equation x′=f(x) has no solution at any point. 相似文献
10.
Vegard Lima 《Journal of Functional Analysis》2004,210(1):148-170
We prove that a Banach space X has the metric approximation property if and only if , the space of all finite rank operators, is an ideal in , the space of all bounded operators, for every Banach space Y. Moreover, X has the shrinking metric approximation property if and only if is an ideal in for every Banach space Y.Similar results are obtained for u-ideals and the corresponding unconditional metric approximation properties. 相似文献
11.
《Quaestiones Mathematicae》2013,36(4):515-524
If X is a Banach space such that Π1(X,l 1) = Π2 (X, l 1), we prove the following results: 1) A bounded sequence (x n ) lies inside the range of some X-valued measure if and only if the operator (α n ) ? l 1 → Σ n α n x n ? X is 1-summing, and 2) If A is a bounded subset of X lying in the range of some X ??-valued measure, then A is necessarily contained in the range of some X-valued measure. 相似文献
12.
《Quaestiones Mathematicae》2013,36(1):105-110
Abstract Let A be a non-empty bounded subset of a locally convex space E. We show that if all the separable subsets of A are weakly metrisable, then the weak*-compact subsets of E1 satisfy geometrical conditions which are similar to the concept of “dentability” used to characterise the Radon-Nikodý Property in dual Banach spaces. 相似文献
13.
Necessary and sufficient conditions are found for the possibility of an extension of Invertibility Symbols from a dense subalgebra to its closure. It is proved that such an extension is possible if and only if the closure does not have any Kakutani elements. The extension of Invertibility Symbols from a Banach algebra to the matrix-valued case is also considered. Algebras with Polynomial Identities play an important role here. Applications to algebras generated by two idempotents and to algebras generated by singular integral operators are suggested. 相似文献
14.
15.
The main objects of study in this paper are Fréchet algebras having an Arens Michael representation in which every Banach algebra is finite dimensional. We shall classify these algebras using a theorem which ensures that the image of any continuous linear map of a Fréchet space of finite type (i.e., for which the defining seminorms have a finite dimensional cokernel) into any Fréchet space is in fact closed.This work is part of the research project of the European Research Training Network Analysis and Operators, contract HPRN-CT 2000 00116, funded by the European Commission. 相似文献
16.
Casey Kelleher 《Topology and its Applications》2012,159(3):749-755
Enflo (1969) [4] constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu (2002) [3] modified Enflo?s example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space (Z,ζ) which is strongly non-embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Our construction is then adapted to show that the group Zω=ℵ0⊕Z admits a Cayley graph which may not be coarsely embedded into any metric space of non-zero generalized roundness. Finally, for each p?0 and each locally finite metric space (Z,d), we prove the existence of a Lipschitz injection f:Z→?p. 相似文献
17.
Danrun Huang 《Integral Equations and Operator Theory》1993,17(1):54-67
For a matrix over a complex commutative unital Banach algebra, necessary and sufficient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earlier work of the author. 相似文献
18.
19.
《Quaestiones Mathematicae》2013,36(3-4):261-267
Abstract We show that the normed space of μ-measurable Pettis integrable functions on a probability space with values in a Banach space X contains a copy of the sequence space c0 if and only if X contains a copy of c0. In this case, if the probability μ has infinite range, a copy of c0 consisting of μ-measurable functions can be found, such that it is complemented in the bigger space of all weakly μ-measurable Pettis integrable functions. 相似文献
20.
Jan van Neerven 《Positivity》2007,11(3):461-467
We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces LXp, where X is a Banach space and 1≤ p<∞, and extend the result to vector-valued Banach function spaces EX, where E is a Banach function space with order continuous norm.
The author is supported by the ‘VIDI subsidie’ 639.032.201 in the ‘Vernieuwingsimpuls’ programme of the Netherlands Organization
for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281. 相似文献